sgpp::optimization::optimizer::AdaptiveNewton Class Reference

Newton method with adaptive step size. More...

#include <AdaptiveNewton.hpp>

Inheritance diagram for sgpp::optimization::optimizer::AdaptiveNewton:

Public Member Functions
	AdaptiveNewton (const AdaptiveNewton &other)
	Copy constructor.
	AdaptiveNewton (const base::ScalarFunction &f, const base::ScalarFunctionHessian &fHessian, size_t maxItCount, double tolerance, double stepSizeIncreaseFactor, double stepSizeDecreaseFactor, double dampingIncreaseFactor, double dampingDecreaseFactor, double lineSearchAccuracy, const base::sle_solver::SLESolver &sleSolver)
	Constructor.
	AdaptiveNewton (const base::ScalarFunction &f, const base::ScalarFunctionHessian &fHessian, size_t maxItCount=DEFAULT_N, double tolerance=DEFAULT_TOLERANCE, double stepSizeIncreaseFactor=DEFAULT_STEP_SIZE_INCREASE_FACTOR, double stepSizeDecreaseFactor=DEFAULT_STEP_SIZE_DECREASE_FACTOR, double dampingIncreaseFactor=DEFAULT_DAMPING_INCREASE_FACTOR, double dampingDecreaseFactor=DEFAULT_DAMPING_DECREASE_FACTOR, double lineSearchAccuracy=DEFAULT_LINE_SEARCH_ACCURACY)
	Constructor.
void	clone (std::unique_ptr< UnconstrainedOptimizer > &clone) const override
double	getDampingDecreaseFactor () const
double	getDampingIncreaseFactor () const
double	getLineSearchAccuracy () const
double	getStepSizeDecreaseFactor () const
double	getStepSizeIncreaseFactor () const
double	getTolerance () const
void	optimize () override
	Pure virtual method for optimization of the objective function.
void	setDampingDecreaseFactor (double dampingDecreaseFactor)
void	setDampingIncreaseFactor (double dampingIncreaseFactor)
void	setLineSearchAccuracy (double lineSearchAccuracy)
void	setStepSizeDecreaseFactor (double stepSizeDecreaseFactor)
void	setStepSizeIncreaseFactor (double stepSizeIncreaseFactor)
void	setTolerance (double tolerance)
	~AdaptiveNewton () override
	Destructor.
Public Member Functions inherited from sgpp::optimization::optimizer::UnconstrainedOptimizer
const base::DataMatrix &	getHistoryOfOptimalPoints () const
const base::DataVector &	getHistoryOfOptimalValues () const
size_t	getN () const
base::ScalarFunction &	getObjectiveFunction () const
base::ScalarFunctionGradient *	getObjectiveGradient () const
base::ScalarFunctionHessian *	getObjectiveHessian () const
const base::DataVector &	getOptimalPoint () const
double	getOptimalValue () const
const base::DataVector &	getStartingPoint () const
void	setN (size_t N)
virtual void	setObjectiveFunction (const base::ScalarFunction &f)
virtual void	setObjectiveGradient (const base::ScalarFunctionGradient *fGradient)
virtual void	setObjectiveHessian (const base::ScalarFunctionHessian *fHessian)
void	setStartingPoint (const base::DataVector &startingPoint)
	UnconstrainedOptimizer (const base::ScalarFunction &f, const base::ScalarFunctionGradient *fGradient, const base::ScalarFunctionHessian *fHessian, size_t N=DEFAULT_N)
	Constructor.
	UnconstrainedOptimizer (const UnconstrainedOptimizer &other)
	Copy constructor.
virtual	~UnconstrainedOptimizer ()
	Destructor.

Static Public Attributes
static constexpr double	DEFAULT_DAMPING_DECREASE_FACTOR = 0.5
	default damping decrease factor
static constexpr double	DEFAULT_DAMPING_INCREASE_FACTOR = 1.0
	default damping increase factor
static constexpr double	DEFAULT_LINE_SEARCH_ACCURACY = 0.01
	default line search accuracy
static constexpr double	DEFAULT_STEP_SIZE_DECREASE_FACTOR = 0.5
	default step size decrease factor
static constexpr double	DEFAULT_STEP_SIZE_INCREASE_FACTOR = 1.2
	default step size increase factor
static constexpr double	DEFAULT_TOLERANCE = 1e-6
	default tolerance
Static Public Attributes inherited from sgpp::optimization::optimizer::UnconstrainedOptimizer
static const size_t	DEFAULT_N = 1000
	default maximal number of iterations or function evaluations

Protected Attributes
const base::sle_solver::GaussianElimination	defaultSleSolver
	default linear solver
double	rhoAlphaMinus
	step size decrease factor
double	rhoAlphaPlus
	step size increase factor
double	rhoLambdaMinus
	damping decrease factor
double	rhoLambdaPlus
	damping increase factor
double	rhoLs
	line search accuracy
const base::sle_solver::SLESolver &	sleSolver
	linear solver
double	theta
	tolerance
Protected Attributes inherited from sgpp::optimization::optimizer::UnconstrainedOptimizer
std::unique_ptr< base::ScalarFunction >	f
	objective function
std::unique_ptr< base::ScalarFunctionGradient >	fGradient
	objective function gradient
std::unique_ptr< base::ScalarFunctionHessian >	fHessian
	objective function Hessian
base::DataVector	fHist
	search history vector (optimal values)
double	fOpt
	result of optimization (optimal function value)
size_t	N
	maximal number of iterations or function evaluations
base::DataVector	x0
	starting point
base::DataMatrix	xHist
	search history matrix (optimal points)
base::DataVector	xOpt
	result of optimization (location of optimum)

Detailed Description

Newton method with adaptive step size.

Constructor & Destructor Documentation

AdaptiveNewton() [1/3]

sgpp::optimization::optimizer::AdaptiveNewton::AdaptiveNewton	(	const base::ScalarFunction &	f,
		const base::ScalarFunctionHessian &	fHessian,
		size_t	maxItCount = DEFAULT_N,
		double	tolerance = DEFAULT_TOLERANCE,
		double	stepSizeIncreaseFactor = DEFAULT_STEP_SIZE_INCREASE_FACTOR,
		double	stepSizeDecreaseFactor = DEFAULT_STEP_SIZE_DECREASE_FACTOR,
		double	dampingIncreaseFactor = DEFAULT_DAMPING_INCREASE_FACTOR,
		double	dampingDecreaseFactor = DEFAULT_DAMPING_DECREASE_FACTOR,
		double	lineSearchAccuracy = DEFAULT_LINE_SEARCH_ACCURACY
	)

Constructor.

By default, GaussianElimination is used to solve the linear systems.

Parameters

f	objective function
fHessian	objective function Hessian
maxItCount	maximal number of function evaluations
tolerance	tolerance
stepSizeIncreaseFactor	step size increase factor
stepSizeDecreaseFactor	step size decrease factor
dampingIncreaseFactor	damping increase factor
dampingDecreaseFactor	damping decrease factor
lineSearchAccuracy	line search accuracy

AdaptiveNewton() [2/3]

sgpp::optimization::optimizer::AdaptiveNewton::AdaptiveNewton	(	const base::ScalarFunction &	f,
		const base::ScalarFunctionHessian &	fHessian,
		size_t	maxItCount,
		double	tolerance,
		double	stepSizeIncreaseFactor,
		double	stepSizeDecreaseFactor,
		double	dampingIncreaseFactor,
		double	dampingDecreaseFactor,
		double	lineSearchAccuracy,
		const base::sle_solver::SLESolver &	sleSolver
	)

Constructor.

Do not destruct the solver before this object!

Parameters

f	objective function
fHessian	objective function Hessian
maxItCount	maximal number of function evaluations
tolerance	tolerance
stepSizeIncreaseFactor	step size increase factor
stepSizeDecreaseFactor	step size decrease factor
dampingIncreaseFactor	damping increase factor
dampingDecreaseFactor	damping decrease factor
lineSearchAccuracy	line search accuracy
sleSolver	reference to linear solver for solving the linear systems (Hessian as coefficient matrix)

AdaptiveNewton() [3/3]

sgpp::optimization::optimizer::AdaptiveNewton::AdaptiveNewton

(

const AdaptiveNewton &

other

)

Copy constructor.

Parameters

other

optimizer to be copied

~AdaptiveNewton()

sgpp::optimization::optimizer::AdaptiveNewton::~AdaptiveNewton ( )

override

Destructor.

Member Function Documentation

clone()

void sgpp::optimization::optimizer::AdaptiveNewton::clone ( std::unique_ptr< UnconstrainedOptimizer > &  clone ) const

overridevirtual

Parameters

[out]

clone

pointer to cloned object

Implements sgpp::optimization::optimizer::UnconstrainedOptimizer.

References clone().

Referenced by clone().

getDampingDecreaseFactor()

double sgpp::optimization::optimizer::AdaptiveNewton::getDampingDecreaseFactor

(

)

const

Returns

damping decrease factor

References rhoLambdaMinus.

getDampingIncreaseFactor()

double sgpp::optimization::optimizer::AdaptiveNewton::getDampingIncreaseFactor

(

)

const

Returns

damping increase factor

References rhoLambdaPlus.

getLineSearchAccuracy()

double sgpp::optimization::optimizer::AdaptiveNewton::getLineSearchAccuracy

(

)

const

Returns

line search accuracy

References rhoLs.

getStepSizeDecreaseFactor()

double sgpp::optimization::optimizer::AdaptiveNewton::getStepSizeDecreaseFactor

(

)

const

Returns

step size decrease factor

References rhoAlphaMinus.

getStepSizeIncreaseFactor()

double sgpp::optimization::optimizer::AdaptiveNewton::getStepSizeIncreaseFactor

(

)

const

Returns

step size increase factor

References rhoAlphaPlus.

getTolerance()

double sgpp::optimization::optimizer::AdaptiveNewton::getTolerance

(

)

const

Returns

tolerance

References theta.

optimize()

void sgpp::optimization::optimizer::AdaptiveNewton::optimize ( )

overridevirtual

Pure virtual method for optimization of the objective function.

The result of the optimization process can be obtained by member functions, e.g., getOptimalPoint() and getOptimalValue().

Implements sgpp::optimization::optimizer::UnconstrainedOptimizer.

References alpha, sgpp::base::DataVector::append(), sgpp::base::DataMatrix::appendRow(), sgpp::base::Printer::disableStatusPrinting(), sgpp::base::DataVector::dotProduct(), sgpp::base::Printer::enableStatusPrinting(), sgpp::optimization::optimizer::UnconstrainedOptimizer::f, sgpp::optimization::optimizer::UnconstrainedOptimizer::fHessian, sgpp::optimization::optimizer::UnconstrainedOptimizer::fHist, sgpp::optimization::optimizer::UnconstrainedOptimizer::fOpt, sgpp::base::Printer::getInstance(), sgpp::base::Printer::isStatusPrintingEnabled(), sgpp::base::DataVector::l2Norm(), lambda, sgpp::optimization::optimizer::UnconstrainedOptimizer::N, sgpp::base::Printer::printStatusBegin(), sgpp::base::Printer::printStatusEnd(), sgpp::base::Printer::printStatusUpdate(), sgpp::base::DataMatrix::resize(), rhoAlphaMinus, rhoAlphaPlus, rhoLambdaMinus, rhoLambdaPlus, rhoLs, sleSolver, sgpp::base::sle_solver::SLESolver::solve(), theta, sgpp::base::DataVector::toString(), sgpp::optimization::optimizer::UnconstrainedOptimizer::x0, sgpp::optimization::optimizer::UnconstrainedOptimizer::xHist, and sgpp::optimization::optimizer::UnconstrainedOptimizer::xOpt.

setDampingDecreaseFactor()

void sgpp::optimization::optimizer::AdaptiveNewton::setDampingDecreaseFactor

(

double

dampingDecreaseFactor

)

Parameters

dampingDecreaseFactor

damping decrease factor

References rhoLambdaMinus.

setDampingIncreaseFactor()

void sgpp::optimization::optimizer::AdaptiveNewton::setDampingIncreaseFactor

(

double

dampingIncreaseFactor

)

Parameters

dampingIncreaseFactor

damping increase factor

References rhoLambdaPlus.

setLineSearchAccuracy()

void sgpp::optimization::optimizer::AdaptiveNewton::setLineSearchAccuracy

(

double

lineSearchAccuracy

)

Parameters

lineSearchAccuracy

line search accuracy

References rhoLs.

setStepSizeDecreaseFactor()

void sgpp::optimization::optimizer::AdaptiveNewton::setStepSizeDecreaseFactor

(

double

stepSizeDecreaseFactor

)

Parameters

stepSizeDecreaseFactor

step size decrease factor

References rhoAlphaMinus.

setStepSizeIncreaseFactor()

void sgpp::optimization::optimizer::AdaptiveNewton::setStepSizeIncreaseFactor

(

double

stepSizeIncreaseFactor

)

Parameters

stepSizeIncreaseFactor

step size increase factor

References rhoAlphaPlus.

setTolerance()

void sgpp::optimization::optimizer::AdaptiveNewton::setTolerance

(

double

tolerance

)

Parameters

tolerance

tolerance

References theta.

Member Data Documentation

DEFAULT_DAMPING_DECREASE_FACTOR

constexpr double sgpp::optimization::optimizer::AdaptiveNewton::DEFAULT_DAMPING_DECREASE_FACTOR = 0.5

staticconstexpr

default damping decrease factor

DEFAULT_DAMPING_INCREASE_FACTOR

constexpr double sgpp::optimization::optimizer::AdaptiveNewton::DEFAULT_DAMPING_INCREASE_FACTOR = 1.0

staticconstexpr

default damping increase factor

DEFAULT_LINE_SEARCH_ACCURACY

constexpr double sgpp::optimization::optimizer::AdaptiveNewton::DEFAULT_LINE_SEARCH_ACCURACY = 0.01

staticconstexpr

default line search accuracy

DEFAULT_STEP_SIZE_DECREASE_FACTOR

constexpr double sgpp::optimization::optimizer::AdaptiveNewton::DEFAULT_STEP_SIZE_DECREASE_FACTOR = 0.5

staticconstexpr

default step size decrease factor

DEFAULT_STEP_SIZE_INCREASE_FACTOR

constexpr double sgpp::optimization::optimizer::AdaptiveNewton::DEFAULT_STEP_SIZE_INCREASE_FACTOR = 1.2

staticconstexpr

default step size increase factor

DEFAULT_TOLERANCE

constexpr double sgpp::optimization::optimizer::AdaptiveNewton::DEFAULT_TOLERANCE = 1e-6

staticconstexpr

default tolerance

defaultSleSolver

const base::sle_solver::GaussianElimination sgpp::optimization::optimizer::AdaptiveNewton::defaultSleSolver

protected

default linear solver

rhoAlphaMinus

double sgpp::optimization::optimizer::AdaptiveNewton::rhoAlphaMinus

protected

step size decrease factor

Referenced by getStepSizeDecreaseFactor(), optimize(), and setStepSizeDecreaseFactor().

rhoAlphaPlus

double sgpp::optimization::optimizer::AdaptiveNewton::rhoAlphaPlus

protected

step size increase factor

Referenced by getStepSizeIncreaseFactor(), optimize(), and setStepSizeIncreaseFactor().

rhoLambdaMinus

double sgpp::optimization::optimizer::AdaptiveNewton::rhoLambdaMinus

protected

damping decrease factor

Referenced by getDampingDecreaseFactor(), optimize(), and setDampingDecreaseFactor().

rhoLambdaPlus

double sgpp::optimization::optimizer::AdaptiveNewton::rhoLambdaPlus

protected

damping increase factor

Referenced by getDampingIncreaseFactor(), optimize(), and setDampingIncreaseFactor().

rhoLs

double sgpp::optimization::optimizer::AdaptiveNewton::rhoLs

protected

line search accuracy

Referenced by getLineSearchAccuracy(), optimize(), and setLineSearchAccuracy().

sleSolver

const base::sle_solver::SLESolver& sgpp::optimization::optimizer::AdaptiveNewton::sleSolver

protected

linear solver

Referenced by optimize().

theta

double sgpp::optimization::optimizer::AdaptiveNewton::theta

protected

tolerance

Referenced by getTolerance(), optimize(), and setTolerance().

---

The documentation for this class was generated from the following files:

• optimization/src/sgpp/optimization/optimizer/unconstrained/AdaptiveNewton.hpp
• optimization/src/sgpp/optimization/optimizer/unconstrained/AdaptiveNewton.cpp